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Butler–Volmer Equation
In electrochemistry, the Butler–Volmer equation (named after John Alfred Valentine Butler and Max Volmer), also known as Tibor Erdey-Grúz, Erdey-Grúz–Volmer equation, is one of the most fundamental relationships in electrochemical kinetics. It describes how the electrical current through an electrode depends on the voltage difference between the electrode and the bulk electrolyte for a simple, unimolecular redox reaction, considering that both a cathodic and an anodic reaction occur on the same electrode: The Butler–Volmer equation The Butler–Volmer equation is: : j = j_0 \cdot \left\ or in a more compact form: :j= j_0 \cdot \left\ where: * j: electrode current density, A/m2 (defined as j ''= I/S'') *j_0: exchange current density, A/m2 * E: electrode potential, V * E_: equilibrium potential, V * T: absolute temperature, K * z: number of electrons involved in the electrode reaction * F: Faraday constant * R: universal gas constant *\alpha_: so-called cathodic char ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrochemistry
Electrochemistry is the branch of physical chemistry concerned with the relationship between Electric potential, electrical potential difference and identifiable chemical change. These reactions involve Electron, electrons moving via an electronically conducting phase (typically an external electrical circuit, but not necessarily, as in Electroless nickel-phosphorus plating, electroless plating) between electrodes separated by an ionically conducting and electronically insulating electrolyte (or ionic chemical species, species in a Solution (chemistry), solution). When a chemical reaction is driven by an electrical Voltage, potential difference, as in electrolysis, or if a potential difference results from a chemical reaction as in an electric battery or fuel cell, it is called an ''electrochemical'' reaction. Unlike in other chemical reactions, in electrochemical reactions electrons are not transferred directly between atoms, ions, or molecules, but via the aforementioned electron ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limiting Case (mathematics)
In mathematics, a limiting case of a mathematical object is a special case that arises when one or more components of the object take on their most extreme possible values. For example: * In statistics, the limiting case of the binomial distribution is the Poisson distribution. As the number of events tends to infinity in the binomial distribution, the random variable changes from the binomial to the Poisson distribution. *A circle is a limiting case of various other figures, including the Cartesian oval, the ellipse, the superellipse, and the Cassini oval. Each type of figure is a circle for certain values of the defining parameters, and the generic figure appears more like a circle as the limiting values are approached. *Archimedes calculated an approximate value of π by treating the circle as the limiting case of a regular polygon with 3 × 2''n'' sides, as ''n'' gets large. *In electricity and magnetism, the long wavelength limit is the limiting case when the wave ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electrochemical Potential
Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference and identifiable chemical change. These reactions involve electrons moving via an electronically conducting phase (typically an external electrical circuit, but not necessarily, as in electroless plating) between electrodes separated by an ionically conducting and electronically insulating electrolyte (or ionic species in a solution). When a chemical reaction is driven by an electrical potential difference, as in electrolysis, or if a potential difference results from a chemical reaction as in an electric battery or fuel cell, it is called an ''electrochemical'' reaction. Unlike in other chemical reactions, in electrochemical reactions electrons are not transferred directly between atoms, ions, or molecules, but via the aforementioned electronically conducting circuit. This phenomenon is what distinguishes an electrochemical reaction from a conventional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reaction Coordinate
In chemistry, a reaction coordinate is an abstract one-dimensional coordinate chosen to represent progress along a reaction pathway. Where possible it is usually a geometric parameter that changes during the conversion of one or more molecular entity, molecular entities, such as bond length or bond angle. For example, in the homolysis (chemistry), homolytic dissociation of molecular hydrogen, an apt choice would be the coordinate corresponding to the bond length. Non-geometric parameters such as Bond order#Non-integer bond orders, bond order are also used, but such direct representation of the reaction process can be difficult, especially for more complex reactions. In computer simulations collective variables are employed for a target-oriented sampling approach. Plain simulations fail to capture so called rare events, because they are not feasible to occur in realistic computation times. This often stems from to high energy barriers separating the reactants from products, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Energy
In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure–volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as G(p,T) = U + pV - TS = H - TS where: * U is the internal energy of the system * H is the enthalpy of the system * S is the entropy of the system * T is the temperature of the system * V is the volume of the system * p is the pressure of the system (which must be equal to that of the surroundings for mechanical equilibrium). The Gibbs free energy change (, measured in joules in SI) is the ''maximum'' amount of non-volume expansion work that can be extracted from a closed system (one that can exchange heat and work with i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reaction Rate Constant
In chemical kinetics, a reaction rate constant or reaction rate coefficient () is a proportionality constant which quantifies the rate and direction of a chemical reaction by relating it with the concentration of reactants. For a reaction between reactants A and B to form a product C, where :A and B are reactants :C is a product :''a'', ''b'', and ''c'' are stoichiometric coefficients, the reaction rate is often found to have the form: r = k mathrmm mathrm Here is the reaction rate constant that depends on temperature, and and are the molar concentrations of substances A and B in moles per unit volume of solution, assuming the reaction is taking place throughout the volume of the solution. (For a reaction taking place at a boundary, one would use moles of A or B per unit area instead.) The exponents ''m'' and ''n'' are called partial orders of reaction and are ''not'' generally equal to the stoichiometric coefficients ''a'' and ''b''. Instead they depend on the reacti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Faraday's Laws Of Electrolysis
Faraday's laws of electrolysis are quantitative relationships based on the electrochemical research published by Michael Faraday in 1833. First law Michael Faraday reported that the mass () of a substance deposited or liberated at an electrode is directly proportional to the charge (, for which the SI unit is the ampere-second or coulomb). m \propto Q \quad \implies \quad \frac = Z Here, the constant of proportionality, , is called the electro-chemical equivalent (ECE) of the substance. Thus, the ECE can be defined as the mass of the substance deposited or liberated per unit charge. Second law Faraday discovered that when the same amount of electric current is passed through different electrolytes connected in series, the masses of the substances deposited or liberated at the electrodes are directly proportional to their respective chemical equivalent/ equivalent weight (). This turns out to be the molar mass () divided by the valence () : \begin & m \propto E; \quad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rate Equation
In chemistry, the rate equation (also known as the rate law or empirical differential rate equation) is an Empirical relationship, empirical Differential equation, differential Expression (mathematics), mathematical expression for the reaction rate of a given reaction in terms of concentrations of chemical species and constant parameters (normally rate coefficients and partial orders of reaction) only. For many reactions, the initial rate is given by a power law such as :v_0\; =\; k[\mathrm]^x[\mathrm]^y where and are the molar concentrations of the species and usually in Mole (unit), moles per liter (molarity, ). The exponents and are the partial ''orders of reaction'' for and , respectively, and the ''overall'' reaction order is the sum of the exponents. These are often positive integers, but they may also be zero, fractional, or negative. The order of reaction is a number which quantifies the degree to which the rate of a chemical reaction depends on concentrations of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tortuosity
Tortuosity is widely used as a critical parameter to predict transport properties of porous media, such as rocks and soils. But unlike other standard microstructural properties, the concept of tortuosity is vague with multiple definitions and various evaluation methods introduced in different contexts. Hydraulic, electrical, diffusional, and thermal tortuosities are defined to describe different transport processes in porous media, while geometrical tortuosity is introduced to characterize the morphological property of porous microstructures. Tortuosity in 2-D Subjective estimation (sometimes aided by optometric grading scales) is often used. The simplest mathematical method to estimate tortuosity is the arc-chord ratio: the ratio of the length of the curve (''C'') to the distance between its ends (''L''): :\tau = \frac Arc-chord ratio equals 1 for a straight line and is infinite for a circle. Another method, proposed in 1999, is to estimate the tortuosity as the integral of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffusion Coefficient
Diffusivity, mass diffusivity or diffusion coefficient is usually written as the proportionality constant between the molar flux due to molecular diffusion and the negative value of the gradient in the concentration of the species. More accurately, the diffusion coefficient times the local concentration is the proportionality constant between the negative value of the mole fraction gradient and the molar flux. This distinction is especially significant in gaseous systems with strong temperature gradients. Diffusivity derives its definition from Fick's law and plays a role in numerous other equations of physical chemistry. The diffusivity is generally prescribed for a given pair of species and pairwise for a multi-species system. The higher the diffusivity (of one substance with respect to another), the faster they diffuse into each other. Typically, a compound's diffusion coefficient is ~10,000× as great in air as in water. Carbon dioxide in air has a diffusion coefficient of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
